There were 744 tickets sold for a basketball game. The activity cardholder's tickets cost $1.75 and the non-cardholders tickets cost $2.25. The total amount of money collected was $1477.50. How many of each kind of ticket were sold?

if there were x cardholders, there were 744-x others. Now add up the money collected for each kind.

1.75x + 2.25(744-x) = 1477.50
1674.00 - 0.5x = 1477.50
x = 393

To solve this problem, we can use a system of equations. Let's assume that the number of activity cardholder tickets sold is represented by 'x' and the number of non-cardholder tickets sold is represented by 'y'.

From the information given, we know that the total number of tickets sold is 744, so we have our first equation:

x + y = 744

We also know that the cost of each activity cardholder ticket is $1.75 and the cost of each non-cardholder ticket is $2.25. The total amount of money collected from ticket sales is $1477.50, so we have our second equation:

1.75x + 2.25y = 1477.50

Now we have a system of equations:

x + y = 744
1.75x + 2.25y = 1477.50

To solve this system, we can use substitution or elimination method. Let's use elimination method.

First, multiply both sides of the first equation by 1.75 to make the coefficients of 'x' in both equations equal:

1.75(x + y) = 1.75(744)
1.75x + 1.75y = 1302

Now, subtract the second equation from this modified equation to eliminate 'x':

(1.75x + 1.75y) - (1.75x + 2.25y) = 1302 - 1477.50
1.75x - 1.75x + 1.75y - 2.25y = -175.50

Simplifying, we get:

-0.5y = -175.50

Dividing both sides of the equation by -0.5, we find:

y = 351

Now we can substitute this value back into any of the original equations to solve for 'x'. Let's use the first equation:

x + y = 744
x + 351 = 744
x = 744 - 351
x = 393

So, there were 393 activity cardholder tickets sold and 351 non-cardholder tickets sold.